Suppose the average fuel economy for the 2013 Ford C Max Hybrid car is reported

Question

Suppose the average fuel economy for the 2013 Ford C Max Hybrid car is reported to be 39.2 miles per gallon (mpg) with a standard deviation of 3.7 mpg. Assume the fuel economy for each tankful of gas for this car follows the normal distribution. Determine the interval of miles per gallon around the mean that include the following:

a. Approximately 68% of the reported fuel economies for this car

b. Approximately 95% of the reported fuel economies for this car Approximately 99.7% of the reported fuel economies for this car

Explanation / Answer

For 68% confidence interval z is 1

For 95% confidence it is 2 and for 99.7% it is 3. This is called empirical rule

We know that the mean is 39.2 and standard deviation is 3.7

a) thus interval will be (39.2-3.7*1,39.2+3.7*1)=(35.5,42.9)

b) for 95% it is (39.2-3.7*2,39.2+3.7*2)=(31.8,46.6)

for 99.7% it is (39.2-3.7*3,39.2+3.7*3)=(28.1,50.3)

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